I was working two sectors combined and I became very busy. There was a plane inbound at 110 and I gave aircraft X a vector to pass behind this aircraft. The assigned heading issued was 230 and climb and maintain 170. Once the aircraft passed behind this aircraft; it needed to be turned westbound due to its route and another aircraft inbound from the south about 20 miles out at 110. This is about the time that I became very busy. I noticed that the two aircraft where at the same altitude on converging courses when they where about seven miles apart. I was not talking to aircraft Y. Issued a traffic alert and aircraft X did not respond. The instructions where for aircraft X to immediately turn right heading 310 this would allow the airplanes to have diverging courses. Aircraft X did not respond I reissued to traffic alert; still no response. I then called the other controller and advised of the situation. Aircraft Y climbed to 117 and aircraft X descended to 105. This resulting in a loss of 1.81 miles and 800 feet. Aircraft X finally responded and said he had aircraft Y in-sight. I continued to work the position for another 20-25 minutes and management was already aware of the situation. Once I got relieved I went to see the OM and he provided me with the distance of loss. I then was sent to another position to relieve another controller who was needed for something else.I made a rookie mistake I should have never given up my altitude until all conflicts were resolved. This should always be the rule no matter how busy you are. As noted above; out of no where I became very busy. I should have kept to the basics.

Title: Controller reports of a situation where he became busy and couldn't turn an aircraft at a specific point and ends up losing separation. Pilot reports of TCAS saving his life.

Narrative: I was working two sectors combined and I became very busy. There was a plane inbound at 110 and I gave Aircraft X a vector to pass behind this aircraft. The assigned heading issued was 230 and climb and maintain 170. Once the aircraft passed behind this aircraft; it needed to be turned westbound due to its route and another aircraft inbound from the south about 20 miles out at 110. This is about the time that I became very busy. I noticed that the two aircraft where at the same altitude on converging courses when they where about seven miles apart. I was not talking to Aircraft Y. Issued a traffic alert and Aircraft X did not respond. The instructions where for Aircraft X to immediately turn right heading 310 this would allow the airplanes to have diverging courses. Aircraft X did not respond I reissued to traffic alert; still no response. I then called the other Controller and advised of the situation. Aircraft Y climbed to 117 and Aircraft X descended to 105. This resulting in a loss of 1.81 miles and 800 feet. Aircraft X finally responded and said he had Aircraft Y in-sight. I continued to work the position for another 20-25 minutes and Management was already aware of the situation. Once I got relieved I went to see the OM and he provided me with the distance of loss. I then was sent to another position to relieve another controller who was needed for something else.I made a rookie mistake I should have never given up my altitude until all conflicts were resolved. This should always be the rule no matter how busy you are. As noted above; out of no where I became very busy. I should have kept to the basics.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.